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An Overview of Self-Consistent Field Calculations Within Finite Basis Sets^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Basis Set Expansion

## 3. Energy Expression

## 4. Unitary Invariance

## 5. Spin-Restriction vs. Unrestriction

## 6. Self-Consistent Field Equations

## 7. Solution of Self-Consistent Field Equations

## 8. Why Does the Self-Consistent Field Method Minimize the Energy?

## 9. Direct Minimization of the Energy

## 10. SCF vs. Direct Minimization

## 11. Density Functional Contributions to Kohn–Sham–Fock Matrix

#### 11.1. LDA Functionals

#### 11.2. GGA Functionals

#### 11.3. Meta-GGA Functionals

#### 11.4. Range-Separated Hybrid Functionals

#### 11.5. Non-Local Correlation

## 12. Summary and Discussion

## Author Contributions

## Funding

## Conflicts of Interest

Sample Availability: Not available. |

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**MDPI and ACS Style**

Lehtola, S.; Blockhuys, F.; Van Alsenoy, C.
An Overview of Self-Consistent Field Calculations Within Finite Basis Sets. *Molecules* **2020**, *25*, 1218.
https://doi.org/10.3390/molecules25051218

**AMA Style**

Lehtola S, Blockhuys F, Van Alsenoy C.
An Overview of Self-Consistent Field Calculations Within Finite Basis Sets. *Molecules*. 2020; 25(5):1218.
https://doi.org/10.3390/molecules25051218

**Chicago/Turabian Style**

Lehtola, Susi, Frank Blockhuys, and Christian Van Alsenoy.
2020. "An Overview of Self-Consistent Field Calculations Within Finite Basis Sets" *Molecules* 25, no. 5: 1218.
https://doi.org/10.3390/molecules25051218